Is the Electric Force in a Shuttling Ball Experiment Balanced?

[Affair]

In my textbook, it states that the ball (neutral) in "Shuttling Ball Experiment" will have induced charge.
Note : The following happens before the ball touches both plates. (There is no conducted charge)

My opinion is : The ball will be attracted to one of the plates. (As there is induced charge)
However, the book states that the electric force (by induced charge) will be balanced. (Stated without proof)

So which one (I or the book) (am / is) wrong ?
If anyone think the book is correct. Can you elaborate the proof here (better with mathematical proof).

 

[kntsy]

In my textbook, it states that the ball (neutral) in "Shuttling Ball Experiment" will have induced charge.
Note : The following happens before the ball touches both plates. (There is no conducted charge)

My opinion is : The ball will be attracted to one of the plates. (As there is induced charge)
However, the book states that the electric force (by induced charge) will be balanced. (Stated without proof)

So which one (I or the book) (am / is) wrong ?
If anyone think the book is correct. Can you elaborate the proof here (better with mathematical proof).

Before the ball touches plate, it is neutral. The induced charges on one side will be balanced by those on the other side. Although there is electric field outside, the electric force acting on the neutral ball is zero.
Note that the ball is stationary initially, you have to apply a force(maybe a slight push) to make it to the plate.
Also note that the ball will decelerate when it is moving towards the plate due to the conservation of energy.

 

[Affair]

Hello Kntsy. Thank you for your reply.

I just wonder what if the ball isn't be placed at the middle (For example : if it is placed close to one plate without touching).
Will it be attracted to the plate due to induced charge ?

In my logic, the induced opposite charge will be closer than the other side of the induced charge. Therefore, the attractive force between the induced opposite charge and the plate will be greater than the repelling force of the induced same charge (on the other side) and the plate.

As a result, isn't that there will be an unbalanced force ?

 

[kntsy]

Hello Kntsy. Thank you for your reply.

I just wonder what if the ball isn't be placed at the middle (For example : if it is placed close to one plate without touching).
Will it be attracted to the plate due to induced charge ?

In my logic, the induced opposite charge will be closer than the other side of the induced charge. Therefore, the attractive force between the induced opposite charge and the plate will be greater than the repelling force of the induced same charge (on the other side) and the plate.

As a result, isn't that there will be an unbalanced force ?

Hi,
As the electric field is uniform between the 2 plates, the electric force does not vary with distance from plates. Therefore, the attractive force and the repulsive force is always balanced no matter where you put the ball.

 

[Affair]

Yes, you are right Kntsy.

The key point is "In uniform field, force is independent of distance"

After further checking my logic, I find that I had a wrong concept. I used to think that force is inverse proportional to the square of distance (coulomb's law). I don't realize that only work on point charge (not a uniform field).

Thank you for solving my problem.